Systems and methods for cell membrane identification and tracking, and technique automation using the same

ABSTRACT

A system including: at least one processor; and at least one memory having stored thereon instructions that, when executed by the at least one processor, control the at least one processor to: receive image data of a sequence of images, and a current image of the sequence of images being after a previous image in the sequence of images, each of the current and previous images including a cell; filter the current image to remove noise; iteratively deconvolve the filtered current image to identify edges of the cell within the current image based on determined edges of the cell within the previous image; and segment the deconvolved current image to determine edges of the cell within the current image.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No. 62/551,570, filed on Aug. 29, 2017, the disclosure of which is herein incorporated by reference in its entirety.

GOVERNMENT SPONSORSHIP

This invention was made with government support under Grant No. 1409422 (CCF-1409422) awarded by the National Science Foundation. The government has certain rights in the disclosure.

BACKGROUND OF THE DISCLOSURE 1. Field of the Disclosure

Embodiments of the present disclosure generally relate to systems and methods for cell membrane identification and tracking and, in particular, cell membrane identification and tracking through using re-weighted total variation dynamic filtering.

2. Background

Live cell imaging allows the monitoring of complex biophysical phenomena as they happen in real time, which is beneficial in studying biological functions, observing drug action, or monitoring disease progression. For these experiments, tissue from an organ such as brain, heart, or liver is sliced and imaged while it is still alive. Fluorescence microscopy is often used for live cell imaging but is not always practical because it requires the use of dyes or genetic engineering techniques to introduce fluorophores into the sample. Instead, it is often desirable to image unlabeled, otherwise optically transparent samples. This is often done using a phase contrast-enhancing technique such as differential interference contrast (DIC) microscopy.

DIC microscopy is widely used for observing unstained biological samples that are otherwise optically transparent. Using machine vision to automatically segment individual cells under DIC optics in real time would be highly useful for microscopy automation of life science experiments. However, precise cell segmentation is challenging, and the related art algorithms are not directly applicable to segmentation under DIC in tissue. Further, identifying relevant features under DIC is challenging. For instance, related art solutions fail to recognize cell-membrane boundaries with sufficient fidelity. Accordingly, certain laboratory techniques have not been able to be efficiently automated.

For example, patch clamping is an important experimental technique of taking high-fidelity electrophysiological measurements from single cells; not only is it considered the “gold” standard for recordings of electrical potentials, it also allows for intercellular access (i.e., extracting or inserting chemical and biological material from it). One method of patch clamping requires a micropipette to be positioned adjacent to a cell's membrane, for a tight seal to be formed using suction between its tip and the cell's membrane. The sheer laboriousness of such manual patch clamping makes automating this process highly advantageous.

Whole-cell patch clamp electrophysiology of neurons in vivo enables the recording of electrical events in cells with great precision and supports a wide diversity of morphological and molecular analysis experiments important for the understanding of single-cell and network functions in the intact brain. In a typical whole-cell patch clamp electrophysiology implementation, a glass pipette electrode is used to gain electrical and molecular access to the inside of a cell. This permits high-fidelity recording of electrical activity in neurons embedded within intact tissue, such as in brain slices, or in vivo. Whole-cell patch clamp recordings of the electrical activity of neurons in vivo, which utilize the glass micropipettes to establish electrical and molecular access to the insides of neurons embedded in intact tissue, exhibit signal quality and temporal fidelity sufficient to report synaptic and ion-channel mediated subthreshold events of importance for understanding how neurons compute, and how their physiology can be modulated by brain disorders or pharmaceuticals. Whole-cell patch clamping of cells in intact tissue also allows for infusion of chemicals and extraction of cell contents. Molecular access to the cell enables infusion of dyes for morphological visualization, as well as extraction of cell contents for transcriptomic single-cell analysis, thus enabling integrative analysis of molecular, anatomical, and electrophysiological information about single neurons in intact tissue. Generally, the patch clamping process is extremely delicate, and the micropipette must be placed just at the cell's boundary, and within tolerances of the robotic actuator (1-2 μm).

It is typical for in vitro brain slice electrophysiology to use DIC microscopy since it is an intrinsic contrast microscopy that does not cause photo-bleaching and phototoxicity, in contrast to exogenous contrast methods like fluorescence microscopy. Cell segmentation on DIC microscopy is especially difficult due to the presence of DIC optical artifacts. Prior work in the DIC cell segmentation literature were found unsuitable in meeting the needs of this particular application. For example, traditional image processing methods for segmentation were applicable only on imagery with extremely low noise. The more sophisticated method of deconvolution was sought since it was able to handle high-noise applications. Other promising and recent variants of DIC deconvolution algorithms exploited structures of smoothness, sparsity, and dynamics for non-linear deconvolution, but they too were not capable of handling the heavy organic interference experienced in this data.

Related-art general purpose segmentation algorithms in the computer vision literature typically assume statistical homogeneity within (or outside) a segmentation region that is lost under contrast-enhancing optical approaches such as DIC. Certain related-art cell segmentation and tracking methods that [7]-[12] are also not directly applicable to cell segmentation under DIC in tissue. For example, algorithms proposed in the Cell Tracking Challenge (CTC) [13], [14] are developed on the CTC dataset that consists only of microscopy imagery of cultured cells (rather than tissue slices) that had minimal organic tissue interference (FIG. 1). These cell-tracking methods (1) often assume simple noise statistics, (2) target gross cell location tracking for mechanobiology tasks (e.g., studies on cell migration, morphology) rather than precise membrane localization, and (3) are designed to be run offline rather than in real time [15].

Recent work on patch clamping has had some success in using a robotic actuator to maneuver the pipette to form the seal (see, e.g., U.S. Pat. No. 9,668,804, US 2018/0028081, and US 2017/0138926, the disclosures of which are incorporated herein by reference in their entireties). While the related art has demonstrated the possibility of automating the patch clamp process by using a motorized robotic actuator to maneuver the probe to the target cell [18], [19], such work has been limited by the related-art methods that do not sufficiently identify and track cell boundaries in real time. For example, several challenges that make cell membrane localization very difficult (e.g., (1) heavy interference from the presence of organic tissue around the target cell, (2) low SNR due to scattering of light characteristic of thick tissue samples, and (3) cell motion induced by the glass probe) are not effectively overcome in the related art.

What is needed, therefore, is a method and system for identifying and tracking cell membranes in high-noise samples that are capable of precisely localizing the cell membranes and performing the localization in real time. It is to such a method and system that embodiments of the present disclosure are directed.

BRIEF SUMMARY OF THE DISCLOSURE

As described herein, there is a great need in the art to identify technologies for identifying and tracking cell membranes and use this understanding to develop novel systems and methods for localizing cell membranes with high precision in real time in samples with heavy organic interference. Certain aspects of the present disclosure satisfy this and other needs.

According to some embodiments there is provided a system including at least one processor; and at least one memory having stored thereon instructions that, when executed by the at least one processor, control the at least one processor to: receive image data of a sequence of images, and a current image of the sequence of images being after a previous image in the sequence of images, each of the current and previous images including a cell; filter the current image to remove noise; iteratively deconvolve the filtered current image to identify edges of the cell within the current image based on determined edges of the cell within the previous image; and segment the deconvolved current image to determine edges of the cell within the current image.

The instructions may further control the at least one processor to identify, within the current image, a subset of the current image containing the cell, deconvolving being performed only the identified subset of the current image.

The instructions may control the at least one processor to iteratively deconvolve the current image by: determining an estimated edge that minimizes a cost function; adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.

The cost function may include a first time corresponding to a predictive error between the current image and an image predicted from the estimated edge, and a second term corresponding to a connectivity determination of the estimated edge within the current image.

The adjusted weights of the cost function may modify the connectivity determination of the estimated edge within the current image. The determined edges of the cell within the previous image may impact the adjusted weights.

The instructions may control the at least one processor to iteratively deconvolve the current image by: iteratively estimate an edge that minimizes a cost function utilizing alternating direction method of multipliers (ADMM); adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.

The instructions may further control the at least one processor to output instructions to an articulating arm to position an instrument proximal to the determined edge of the current image. The instrument may include one or more of: an electrode; an injector; and a manipulation instrument.

The instructions may further control the at least one processor to: set the current image as the previous image; set a next image in the sequence of images as the current image; and repeat the filtering, iteratively deconvolving, and segmenting.

The sequence of image comprises a live video; and the edges of the cell within the current image are determined in near real-time.

According to some embodiments there is provided a method including: receiving image data of a sequence of images, and a current image of the sequence of images being after a previous image in the sequence of images, each of the current and previous images including a cell; filtering the current image to remove noise; iteratively deconvolving the filtered current image to identify edges of the cell within the current image based on determined edges of the cell within the previous image; and segmenting the deconvolved current image to determine edges of the cell within the current image.

The method may further include identifying, within the current image, a subset of the current image containing the cell, deconvolving being performed only the identified subset of the current image.

The method may include iteratively deconvolving the current image by: determining an estimated edge that minimizes a cost function; adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.

The cost function may include a first time corresponding to a predictive error between the current image and an image predicted from the estimated edge, and a second term corresponding to a connectivity determination of the estimated edge within the current image.

The adjusted weights of the cost function may modify the connectivity determination of the estimated edge within the current image, and the determined edges of the cell within the previous image may impact the adjusted weights.

The method may include deconvolving the current image by: iteratively estimate an edge that minimizes a cost function utilizing alternating direction method of multipliers (ADMM); adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.

The method may further include moving an articulating arm to position an instrument proximal to the determined edge of the current image.

The method may further include: setting the current image as the previous image; setting a next image in the sequence of images as the current image; and repeating the filtering, iteratively deconvolving, and segmenting.

The sequence of image comprises a live video; and the edges of the cell within the current image are determined in near real-time.

These and other objects, features and advantages of the present disclosure will become more apparent upon reading the following specification in conjunction with the accompanying description, claims and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying. Figures, which are incorporated in and constitute a part of this specification, illustrate several aspects described below. The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

FIG. 1 depicts example images obtained with DIC microscopy (40× magnification). Left panel: cultured human embryonic kidney (HEK293) cell. Right panel: neuron in mouse brain tissue (400 um thickness). The image on the right has high levels of imaging noise due to light scatter and interference due to organic material in surrounding tissue. Scale bar 10 μm.

FIG. 2 depicts the example stages of the described imaging system. The full imaging system has three stages: patch tracking, deconvolution, and segmentation. In patch tracking, a user-defined template is provided for template matching and tracking spatial coordinates over time with a Kalman filter. In deconvolution, the patch is deconvolved to infer the OPL approximation. In segmentation, a global threshold is applied to yield a binary segmentation mask to determine the cell membrane location.

FIG. 3 shows radially averaged power density spectrum (RAPSD) plots in log-scale from an example 64×64 cell patch. The Wiener filter utilized an approximation to the signal (in blue) and the signal-with-noise (in red) power spectral density modeled as a linear polynomial least-square fitting over the radially averaged power spectral density (RAPSD). The signal approximation was computed by averaging the power spectral density of simulated cells. The signal-with-noise approximation was extracted from an observed patch. The final filtered spectrum is shown in black.

FIG. 4 shows the contribution of pre-filtering seen as interference-suppression. The first column of images pertains to the ground truth simulation. The second and third columns pertain to PF+RWTV-DF performed without and with the pre-filter respectively. While the pre-filter blurred high frequency interference content, it also blurred the cell's edges. The pre-filtered observation has its edge integrity retained while suppressing surrounding interference found at the bottom left corner and immediate right of the cell; this results in an overall segmentation that is closer to the ground truth.

FIG. 5 shows a graphical model depicting the hierarchical Laplacian scale mixture model's Bayesian prior dependencies in the RWTV-DF algorithm. Prior state estimates of the signal edges were used to set the hyper-priors for the second level variables (i.e., variances of the state estimates), thereby implementing a dynamical filter that incorporates edge information into the next time step.

FIG. 6 shows the ground truth image that was the binary mask of a simulated image. Subsequent images reflected the iterations of reweighting process during deconvolution (iterations 1 through 5 respectively). Over the iterations, dominant edges were enhanced while weaker ones recede, resulting in piecewise smooth solutions that are amenable to segmentation.

FIG. 7 shows a block diagram of the cell simulator. Gray blocks: generative models that learn from available data. White blocks: generative models that rely on user-parameters. The respective images are outputs from the various stages of the simulator, including (i) Binary image of synthetic cell shape (ii) Textured OPL image showing light transmission through tissue (iii) Received image through DIC optics and (iv) Final image with noise and interference.

FIG. 8 shows quantile-quantile plots visualized similarities between the characteristics of simulated and actual cell-shapes. Distributions were compared for the following shape-features: aspect ratio (top left), form factor (top right), convexity (bottom left), and solidity (bottom right) as defined in the text. (c-1, c-2, d-1, d-2) Several outlier pairs from the convexity and solidity plots are identified and shown. The outlier pairs appeared to be caused by actual cell shape outlier statistics that are underrepresented (due to lack of training examples) and thus not fully captured by the model.

FIG. 9A-9B show the general qualitative similarity between randomly drawn samples of (9A) synthetically generated DIC cell images using the proposed simulator, and (9B) actual DIC microscopy images of rodent neurons. Similarities in imagery characteristics included: (1) DIC optical features as shown by the 3D relief which were highlighted by the high/low intensity ‘shadows’ in the cell edges, (2) organic interference which appeared as Gaussian noise with a frequency profile (further elaboration on quantitative similarities are found in the Appendix, (3) cell shapes as demonstrated by the cell shapes' organic and natural contours, and (4) uneven lighting bias as shown by the smooth but uneven background gradient.

FIG. 10 shows boundary error metrics. Each blue line l_(a) represents an approach direction of a pipette towards the ground truth centroid. p_(a,B) represents the point where the algorithm thinks the membrane is. Individual boundary errors are computed as the distance ∥p_(a,B)−p_(a)∥₂ and represented as black dotted lines. The average of all errors constitutes the Average Boundary Error (ABE), the maximum constitutes the Maximum Boundary Error (MBE), and the variance of errors constitutes the Variance of Boundary Errors (VBE).

FIG. 11 shows average boundary errors (ABE), maximum boundary errors (MBE), and variance of boundary errors (VBE) for each of the algorithms across 100 video trials of simulated data. ABE/MBENBE was aggregated from 100 frames of 100 trials (i.e., 10,000 data points). The PF+RWTV-DF algorithm was found to have a state-of-the-art performance, showing statistically significant improvements in ABE/MBE/VBE compared to other algorithms (p≤0.001, denoted by the 3 stars based on paired t-tests).

FIG. 12A-12E show ABE, MBE, and VBE evolving with time are shown from (12A) to (12C) (respectively) for a single representative video (Trial #4) of a simulated DIC microscopy cell with 100 video frames after deconvolution and segmentation using four different algorithms. The images in (12D) are snapshots of the deconvolution output at frame 100, and the images in (12E) are their respective segmentations.

FIG. 13A-13C show three example image patches of real cell data were deconvolved using four algorithms and the resulting segmentations (top row of FIGS. 13A, 13B and 13C) and deconvolutions (bottom row of FIGS. 13A, 13B and 13C) are displayed. Segmentations were obtained from deconvolution by global thresholding using Otsu's method [45]. The proposed PF+RWTV-DF algorithm performs consistently well even in severe interference (defined by the degree of distortion around the edges and surface undulations within the cell).

FIG. 14A-14C depict snapshots from real video data of a cell undergoing patch clamping that demonstrated the efficacy of the proposed pipette removal method (via inpainting). The pipette mask is outlined in red while the cell segmentation is outlined in blue. Each snapshot illustrated varying degrees of overlap between the pipette and the cell: (14A) the pipette is far from the cell, (14B) the pipette is in close proximity to the cell, and (14C) the pipette is “touching” the cell. The efficacy of the proposed inpainting method for pipette removal (versus no inpainting) is qualitatively demonstrated by its ability to cleanly segment the cell despite the pipette's presence.

FIG. 15A-15B show the visual similarities that were observed between the (15A) synthetically generated cell-shapes, and the (15B) cell-shapes extracted from DIC imagery of rodent brain slices.

FIG. 16A-16D show (16A) synthetically generated organic noise (synthetic) (16B) An image patch of organic noise from a real DIC image (i.e. an image patch with no cell, only noise) (16C) Comparisons of pixel intensity distributions (16D) Comparisons of radially averaged power spectral density.

FIG. 17 shows four snapshots in time (indexed by k) from a synthesized video (of 100 frames), generated from a single cell image. The cell's motion induced by external forces (i.e., pipette motion, though not explicitly present) is simulated by a slight contraction followed by expansion over time, while performing a linear translation, from left to right of the frame. Synthetic interference (simulating organic material) shows up as a high-intensity blob around the bottom left corner of the cell, interfering with the cell's edges.

FIG. 18 illustrates deconvolution with inpainting for a single cell with different iterations of ADMM between reweighing according to an example implementation of the present disclosure.

FIG. 19 shows aggregated statistics of RWTV-ADMM across for different iterations of ADMM between reweighing over 100 trials according to an example implementation of the present disclosure.

FIG. 20 illustrates an environment in which one or more aspects of the present disclosure may be implemented.

FIG. 21 is a block diagram of an example computer system capable of implementing certain aspects of the present disclosure.

DETAILED DESCRIPTION OF THE DISCLOSURE

Certain aspects of the present disclosure are described herein with reference to cell membrane identification and tracking for patch clamping, this is merely an example, and aspects of the present disclosure may be used in various circumstances. For example, in some cases, cell membrane identification and tracking according to the present disclosure may be utilized in individual cell manipulation or injection. Moreover, aspects of the present disclosure are related to DIC microscopy images. However, one of ordinary skill will recognize that aspects of the present disclosure may be utilized for different optic models by changing the optic model.

Differential interference contrast (DIC) microscopy is widely used for observing unstained biological samples that are otherwise optically transparent. Combining this optical technique with machine vision could enable the automation of many life science experiments; however, identifying relevant features under DIC is often challenging. In particular, precise tracking of cell boundaries in a thick (>100 μm) slice of tissue has not previously been accomplished. Herein is described a novel deconvolution algorithm that identifies and tracks these membrane locations.

Certain implementations provide cell segmentation and boundary tracking for DIC imagery of tissue slices. One of ordinary skill will recognize that certain aspects of the present disclosure may be utilized in various tasks. However, for ease of description, certain portions of the present disclosure are related to patch-clamp recording in brain tissue. In this experimental paradigm, brain tissue was sliced into 100-400 μm thick sections, each containing thousands of neurons embedded in a dense biological milieu. The slice was imaged with a microscope and glass probe was inserted into the tissue to sample the electrical activity of individual cells [16], [17].

According to some embodiments, deconvolution of an image of a cell is performed to find a cell boundary. Certain aspects of the present disclosure may involve, as non-limiting examples, patch tracking, deconvolution, and segmentation. Patch tracking may include performing pattern recognition on portion of an image to identify a general area likely to contain cell boundaries (e.g., a cell). In some implementations, patch tracking may not be performed, and deconvolution may be performed on an entirety of an image or one or more subsets thereof. In some cases, the pre-filtering may remove noise from an organic image (e.g., an image of a brain slice). The pre-filtering may be tuned to statistical characteristics of a specific imaging technique and tissue sample and/or type.

Deconvolution may utilize two-stages, pre-filtering (PF) and Re-Weighted Total Variation Dynamic Filtering (RWTV-DF). In some cases, the deconvolution may be performed on pre-filtered or unfiltered data. As discussed below in greater detail, the deconvolution may identify cell edges based on how well predicted edges describe the image data (e.g., least means square) and how connected the various edges are (e.g., by minimizing a summation of spatial derivatives of the image). The deconvolution may be applied to a sequence of images (e.g., video) and the derivatives may be weighted based on detected edges in a prior image in the sequence. The deconvolution may be iteratively performed, adjusting weights based on predicted edges, and then re-predicting the edges.

Definitions

To facilitate an understanding of the principles and features of the various embodiments of the disclosure, various illustrative embodiments are explained below. Although exemplary embodiments of the disclosure are explained in detail, it is to be understood that other embodiments are contemplated. Accordingly, it is not intended that the disclosure is limited in its scope to the details of construction and arrangement of components set forth in the following description or examples. The disclosure is capable of other embodiments and of being practiced or carried out in various ways. Also, in describing the exemplary embodiments, specific terminology will be resorted to for the sake of clarity.

It must also be noted that, as used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural references unless the context clearly dictates otherwise. For example, reference to a component is intended also to include composition of a plurality of components. References to a composition containing “a” constituent is intended to include other constituents in addition to the one named. In other words, the terms “a,” “an,” and “the” do not denote a limitation of quantity, but rather denote the presence of “at least one” of the referenced item.

As used herein, the term “and/or” may mean “and,” it may mean “or,” it may mean “exclusive-or,” it may mean “one,” it may mean “some, but not all,” it may mean “neither,” and/or it may mean “both.” The term “or” is intended to mean an inclusive “or.”

Also, in describing the exemplary embodiments, terminology will be resorted to for the sake of clarity. It is intended that each term contemplates its broadest meaning as understood by those skilled in the art and includes all technical equivalents which operate in a similar manner to accomplish a similar purpose. It is to be understood that embodiments of the disclosed technology may be practiced without these specific details. In other instances, well-known methods, structures, and techniques have not been shown in detail in order not to obscure an understanding of this description. References to “one embodiment,” “an embodiment,” “example embodiment,” “some embodiments,” “certain embodiments,” “various embodiments,” etc., indicate that the embodiment(s) of the disclosed technology so described may include a particular feature, structure, or characteristic, but not every embodiment necessarily includes the particular feature, structure, or characteristic. Further, repeated use of the phrase “in one embodiment” does not necessarily refer to the same embodiment, although it may.

Ranges may be expressed herein as from “about” or “approximately” or “substantially” one particular value and/or to “about” or “approximately” or “substantially” another particular value. When such a range is expressed, other exemplary embodiments include from the one particular value and/or to the other particular value. Further, the term “about” means within an acceptable error range for the particular value as determined by one of ordinary skill in the art, which will depend in part on how the value is measured or determined, i.e., the limitations of the measurement system. For example, “about” can mean within an acceptable standard deviation, per the practice in the art. Alternatively, “about” can mean a range of up to ±20%, preferably up to ±10%, more preferably up to ±5%, and more preferably still up to ±1% of a given value. Alternatively, particularly with respect to biological systems or processes, the term can mean within an order of magnitude, preferably within 2-fold, of a value. Where particular values are described in the application and claims, unless otherwise stated, the term “about” is implicit and in this context means within an acceptable error range for the particular value.

Throughout this disclosure, various aspects of the disclosure can be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the disclosure. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 2.7, 3, 4, 5, 5.3, and 6. This applies regardless of the breadth of the range.

Similarly, as used herein, “substantially free” of something, or “substantially pure”, and like characterizations, can include both being “at least substantially free” of something, or “at least substantially pure”, and being “completely free” of something, or “completely pure”.

By “comprising” or “containing” or “including” is meant that at least the named compound, element, particle, or method step is present in the composition or article or method, but does not exclude the presence of other compounds, materials, particles, method steps, even if the other such compounds, material, particles, method steps have the same function as what is named.

Throughout this description, various components may be identified having specific values or parameters, however, these items are provided as exemplary embodiments. Indeed, the exemplary embodiments do not limit the various aspects and concepts of the present disclosure as many comparable parameters, sizes, ranges, and/or values may be implemented. The terms “first,” “second,” and the like, “primary,” “secondary,” and the like, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another.

It is noted that terms like “specifically,” “preferably,” “typically,” “generally,” and “often” are not utilized herein to limit the scope of the claimed disclosure or to imply that certain features are critical, essential, or even important to the structure or function of the claimed disclosure. Rather, these terms are merely intended to highlight alternative or additional features that may or may not be utilized in a particular embodiment of the present disclosure. It is also noted that terms like “substantially” and “about” are utilized herein to represent the inherent degree of uncertainty that may be attributed to any quantitative comparison, value, measurement, or other representation.

The dimensions and values disclosed herein are not to be understood as being strictly limited to the exact numerical values recited. Instead, unless otherwise specified, each such dimension is intended to mean both the recited value and a functionally equivalent range surrounding that value. For example, a dimension disclosed as “50 mm” is intended to mean “about 50 mm.”

It is also to be understood that the mention of one or more method steps does not preclude the presence of additional method steps or intervening method steps between those steps expressly identified. Similarly, it is also to be understood that the mention of one or more components in a composition does not preclude the presence of additional components than those expressly identified.

The materials described hereinafter as making up the various elements of the present disclosure are intended to be illustrative and not restrictive. Many suitable materials that would perform the same or a similar function as the materials described herein are intended to be embraced within the scope of the disclosure. Such other materials not described herein can include, but are not limited to, materials that are developed after the time of the development of the disclosure, for example. Any dimensions listed in the various drawings are for illustrative purposes only and are not intended to be limiting. Other dimensions and proportions are contemplated and intended to be included within the scope of the disclosure.

EXAMPLES

The present disclosure is also described and demonstrated by way of the following examples. However, the use of these and other examples anywhere in the specification is illustrative only and in no way limits the scope and meaning of the disclosure or of any exemplified term. Likewise, the disclosure is not limited to any particular preferred embodiments described here. Indeed, many modifications and variations of the disclosure may be apparent to those skilled in the art upon reading this specification, and such variations can be made without departing from the disclosure in spirit or in scope. The disclosure is therefore to be limited only by the terms of the appended claims along with the full scope of equivalents to which those claims are entitled.

Example 1: Cell Membrane Tracking in Living Brain Tissue Using DIC Microscopy

The inventors' proposed algorithm extended the framework provided by [20] and was formulated as a regularized least-squares optimization that incorporates a filtering mechanism to handle organic tissue interference and a robust edge-sparsity regularizer that integrates dynamic edge-tracking capabilities. The described algorithm performed a deconvolution of the complex effects of DIC imaging integrated into a segmentation process and was not a direct segmentation of raw DIC images. Toward this end, the focus of this algorithm was specifically on cell boundary tracking instead of more typical deconvolution metrics such as least-square image reconstruction.

Also described herein is a MATLAB toolbox for accurately simulating DIC microscopy images of in vitro brain slices. Building on existing DIC optics modelling, the inventors' simulation framework additionally contributed an accurate representation of interference from organic tissue, neuronal cell-shapes, and tissue motion due to the action of the pipette. This simulator allows users to better understand the image statistics to improve algorithms, as well as quantitatively test cell segmentation and tracking algorithms in scenarios where ground truth data is fully known. The simulation toolbox is freely available under GNU GPL at siplab.gatech.edu.

A. DIC Microscopy

DIC microscopy can enhance the contrast of an image by exploiting the fact that differences in the tissue often have different optical transmission properties that can be measured through the principle of interferometry. Specifically, the signal that is reconstructed by the algorithm is known as the optical path length (OPL) signal image, which is proportional to the underlying phase-shift. The OPL is defined as the product of refractive index and thickness distributions of the object relative to the surrounding medium [20], [21]. This OPL signal was denoted as x_(k)∈

^(N) (a vectorized form of the √N×√N OPL image's intensity values) and indexed in time by subscript k. DIC microscopy was used to amplify differences between the cell's refractive index and its environment to enhance visibility of the cell, thus highlighting edge differentials and giving the appearance of 3D relief. This effect can be idealized as a convolution between the optics' point spread function and the OPL, and denoted as Dx_(k), where D∈

^(N×N) is a matrix that captures the 2D convolution against a kernel d ∈

^(K×K).

While more sophisticated DIC imaging models (c.f., [22]) exist, for means of example, a kernel d corresponding to an idealized DIC model proposed by Li and Kanade [20] which is a steerable first-derivative of Gaussian kernel may be used:

$\begin{matrix} {{{d\left( {x,y} \right)} \propto {{{- x}\mspace{14mu}{{\cos(\theta)} \cdot e^{- \frac{x^{2} + y^{2}}{\sigma_{d}^{2}}}}} - {y\mspace{14mu}{{\sin(\theta)} \cdot e^{- \frac{x^{2} + y^{2}}{\sigma_{d}^{2}}}}}}},} & (1) \end{matrix}$ where σ_(d) refers to the Gaussian spread and θ_(d) refers to a steerable shear angle. This model assumed an idealized effective point spread function (EPSF), where the condenser lens is infinite-sized and the objective is infinitely small (with respect to the wavelength). This model also ignored any phase wrapping phenomenon by assuming that the specimen is thin enough or the OPL varies slowly enough such that it behaves in the linear region of the phase difference function [22]. In practice, d(x, y) is discretized as d with a proportionality constant of 1, and with x and y each taking the discrete domain

$\left\{ {{- \frac{K - 1}{2}},{- \frac{K - 3}{2}},\ldots\mspace{14mu},\frac{K - 3}{2},\frac{K - 1}{2}} \right\}.$

DIC cell segmentation algorithms generally fall into three categories: direct, machine-learned, or deconvolution (or phasereconstruction) algorithms. Direct algorithms apply standard image processing operations such as low-pass filtering, thresholding, and morphological shape operations [5], [6], [23] but often are not robust and commonly work optimally on very low-noise/interference imagery. Machine-learned algorithms perform statistical inference learned from a large number of cell-specific training images (e.g., deep convolutional networks [24] or Bayesian classifiers [25]). Such algorithms have been shown to perform coarse segmentation surprisingly well in challenging scenarios (e.g., cells with complicated internal structures with low-noise/interference) for applications like cell-lineage tracking or cell-counting, yet they appear to lack precision for accurate cell-boundary localization. Certain related art deconvolution algorithms may be effective at retrieving the OPL for noisy microscopy images with little interference. However, organic tissue interference surrounding the cell negatively affected the reconstruction (and subsequently segmentation), especially around the edges of the cell.

Meanwhile, reweighted l1 framework introduced by Candes et al. [31] was found to produce robust reconstructions because each signal element's statistics were individually parameterized as opposed to having them globally parameterized by a single term (in the non-weighted 1 setup). This method, though very effective for the tracking of sparsely distributed signals, may not be directly applied since the signal space (i.e., the DIC imagery) distribution is inadequately sparse. Likewise, the reweighted TV minimization introduced in [31] as a regularization method (in compressive sensing), for recovering the Shepp-Logan phantom [34] from sparse Radon projections, demonstrating potential for application in bioimagery, is not capable of exploiting dynamical information in temporal data.

One of ordinary skill will understand that this is merely an example, and aspects of the disclosure may be applied to various imaging models.

B. Cell Simulator

Accurate cell simulators are a valuable tool for two reasons: they allow objective testing with known ground truth and provide insights into generative models that facilitate algorithm development. Currently, the vast majority of existing cell simulator packages focus specifically on fluorescence microscopy [35]-[39] rather than DIC microscopy. While some simulators [36], [37] excelled at providing a large variety of tools for simulating various experimental scenarios and setups, most lacked simulation of synthetic cellular noise similar to that found in DIC microscopy images of brain slices (due to the presence of cellular tissue). Most simulators tend to target very specific types of cells [35], [36], [39] and there have been initial efforts to organize and share cellular information (e.g., spatial, shape distributions) into standardized formats across simulators [15], [16]. Despite this, no existing simulator currently generates synthetic DIC imaging of neurons such as those used in patch clamp experiments for brain slices. To facilitate algorithm design and evaluation on the important problem of automated patch clamping, the inventors have built and released MATLAB toolbox for accurately simulating DIC microscopy images of in vitro brain slices (described in the Appendix and freely available under GNU GPL at siplab.gatech.edu).

Formulation of the Deconvolution Algorithm

Certain aspects of the described systems and methods are designed to provide automated visual tracking of the membrane of a user-selected target cell (e.g., to guide a robotic patch clamping system). According to some embodiments, three general stages visualized by FIG. 2 are used. The first stage includes computer vision tracking techniques to identify the general patch of interest containing the target cell on the current frame (e.g., a current image of a video containing the cell). The second stage implements dynamic deconvolution to recover a time-varying OPL image that can be used for segmentation. In some cases, good performance is retained when a foreign object (e.g., a recording pipette) overlaps with the cell by removing the foreign object from the image and performing inpainting. The third stage includes a segmentation on the output of the deconvolution, which was performed with simple thresholding. It is suggested that a simple segmentation strategy is sufficient after a robust deconvolution process.

Through the first stage, the deconvolution and segmentation algorithms may be run on a limited image patch size (e.g., 64×64, as a trade-off between speed and resolution) that was found by tracking gross motion in the image. For example, template matching (via normalized cross-correlation) may be performed on each frame using a user-selected patch (e.g., obtained via a mouse-click to associate coordinates of the image patch center with the targeted cell's center). Patch-tracking robustness may be improved by running a standard Kalman filter on the positional coordinates of the found patch (i.e., tracking a two-dimensional state vector of the horizontal and vertical location of the patch center). To increase efficacy with the correlation approach, a pre-processing stage may be used, for example, to eliminate lighting bias (i.e., uneven background subtraction) on each video frame. In some cases, quadratic least squares estimation (with a polynomial order of 2) may be used, but this is merely an example. In some cases, bias elimination may be applied to an entire video frame (rather than to each patch) for computational efficiency. Also, if the bias conditions were static throughout a video or multiple frames, the bias or other pre-filtering may be computed once, cached, then applied across multiple frames. While tracking the detailed cell membrane locations is challenging in the related art, tracking the general location of the patch containing the target cell can be done with very high accuracy.

Formulation of the Pre-Filtered Re-Weighted Total Variation Dynamic Filtering (PF+RWTV-DF) Algorithm

Certain aspects of the present disclosure relate to a Pre-Filtered Re-Weighted Total Variation Dynamic Filtering (PF+RWTV-DF) algorithm constructed of two distinct components: a pre-filtering (PF) operation, and the re-weighted total variation dynamic filtering (RWTV-DF) deconvolution algorithm. The two parts played distinct yet important roles: PF performed interference suppression while the RWTV-DF deconvolution achieved dynamic edge-sparse reconstructions. However, this is merely an example and, in some cases, the RWTV-DF may be utilized without PF.

1) Pre-Filtering: The presence of non-white Gaussian noise due to organic tissue interference caused challenges in recognizing membrane boundaries. In some instances, PDF may be used to estimate the interference-free observation, for example, by “whitening” the spectra associated with the observation and amplifying the spectra associated with the signal. Specifically, in some cases, the PF filter's design was derived using the Wiener filter and given in the spatial-frequency domain by:

$\begin{matrix} {{\left| F_{k} \right|^{2} = {\frac{\left| {\mathcal{F}{\left\{ d \right\} \cdot {\hat{X}}_{k}}} \right|^{2}}{\left| {\mathcal{F}{\left\{ d \right\} \cdot {\hat{X}}_{k}}} \middle| {}_{2}{+ \left| {\hat{N}}_{k} \right|^{2}} \right.} = \frac{\left| {\mathcal{F}{\left\{ d \right\} \cdot {\hat{X}}_{k}}} \right|^{2}}{\left| {\hat{Y}}_{k} \right|^{2}}}},} & (6) \end{matrix}$ where F_(k) is the spatial Fourier spectrum of the pre-filter,

{d} is the spatial Fourier transform of the DIC imaging function from Eq. (1), X_(k) is the OPL signal's spatial Fourier spectrum estimate, N_(k) is the spatial Fourier spectrum estimate of n_(organic) ^(k) combined with n_(sensor) ^(k) and Ŷ_(k) is the signal-plus-noise's spatial Fourier spectrum estimate. The inventors estimated all spatial Fourier spectra using least-squares polynomial fits of the radially averaged power spectral density (RAPSD), defined as a radial averaging of the DC-centered spatial-frequency power spectrum density. Intuitively, this estimated an image's underlying spectrum via a form of direction-unbiased smoothing. Specifically, the inventors estimated the signal-only component X_(k) from averaged RAPSDs from OPLs of simulated cells generated from the realistic simulation framework described herein, and estimated the combined signal-plus-noise spectra Ŷ_(k) from RAPSDs of observed images y_(k). FIG. 3 illustrates the estimation process and effect of the pre-filter in the frequency domain. The positive contribution of the prefilter was highlighted in FIG. 4 in the segmentation algorithm described below. 2) RWTV-DF

Given the edge-sparse nature of the data and the particular need for accuracy in the cell membrane locations during segmentation (in contrast to the more typical MSE minimization of the deconvolved image), the TV norm may be used as the core regularization approach [46] for this algorithm. Specifically, in some cases, the calculated isotropic TV may be taken as:

${{x_{k}}_{TV} = {{\sum\limits_{i = 1}^{N}{{T_{i}x_{k}}}_{2}} = {\sum\limits_{i = 1}^{N}{t_{k}\lbrack i\rbrack}}}},$ where T_(i) ∈

^(2×N) is an operator that extracts the horizontal and vertical forward-differences of the i-th pixel of x_(k) into an

² vector, whose l2 norm is denoted as an individual edge-pixel t_(k)[i]. This basic regularizer was improved in [31] via an iterative estimation of weights on the individual edges through a Majorize-Minimization algorithm. However, this regularizer does not incorporate any dynamical information for the tracking of moving edges.

To address this issue, a hierarchical Bayesian probabilistic model where dynamics are propagated via second-order statistics from one-time step to the next may be used designed such that the described method operates solely in the edge-pixel space. As will be understood in light of the present disclosure, the sparse edge locations at the previous frame provided strong evidence that there could be an edge nearby in the current frame. Edge locations may be modeled with a sparsity-inducing probability distribution with a parameter controlling the spread (i.e., variance) of the distribution. When previous data gave evidence for an edge in a given location, the parameter to increase the variance of the prior data in this location, thereby likely making it easier for the inference to identify the presence of the edge from limited observations. In contrast, when previous data indicated that an edge in a location was unlikely, this variance may be decreased thereby requiring more evidence from the observations to infer the presence of an edge.

As a non-limiting example, at the lowest level of the hierarchy, the pre-filtered observations may be modeled conditioned on the OPL signal x_(k) with a white Gaussian distribution:

$\begin{matrix} {{{p\left( {F_{k}y_{k}} \middle| x_{k} \right)} \propto e^{{- \frac{1}{2\sigma^{2}}}{{{F_{k}y_{k}} - {Dx}_{k}}}_{2}^{2}}},} & (7) \end{matrix}$ where F_(k) is the matrix operator describing 2D convolution (in the frequency domain) against the pre-filter F_(k) described earlier by Eq. (6). At the next level, the individual edge-pixels t_(k)[i] may be assumed sparse and therefore best modeled with a distribution with high kurtosis but with unknown variance. One of ordinary skill will recognize that aspects of the present disclosure may be utilized for different optic models (i.e., optic models besides DIC) by modifying F_(k) to fit the different optical models. Conditioning on a weighting γ_(k)[i] that controlled the individual variances, the t_(k)[i] may be modeled as random variables arising from independent Laplacian distributions:

$\begin{matrix} {{{p\left( {t_{k}\lbrack i\rbrack} \middle| {\gamma_{k}\lbrack i\rbrack} \right)} = {\gamma_{0}\frac{\gamma_{k}\lbrack i\rbrack}{2}e^{{{- \gamma_{0}}{{\gamma_{k}{\lbrack i\rbrack}} \cdot {t_{k}{\lbrack i\rbrack}}}}|}}},} & (8) \end{matrix}$ where γ₀ is a positive constant. At the top-most level, the weights γ_(k)[i] are themselves also treated as random variables with a Gamma hyperprior:

$\begin{matrix} {{{p\left( {\gamma_{k}\lbrack i\rbrack} \middle| {\theta_{k}\lbrack i\rbrack} \right)} = {\frac{\gamma_{k}^{a - 1}}{{\theta_{k}^{\alpha}\lbrack i\rbrack}{\Gamma(a)}}e^{{- {\gamma_{k}{\lbrack i\rbrack}}}/{\theta_{k}{\lbrack i\rbrack}}}}},} & (9) \end{matrix}$ where α is a positive constant, Γ(·) is the Gamma function, and θ_(k)[i] is the scale variable that controls the Gamma distribution's mean and variance over γ_(k)[i]. This top-level variable may be used to insert a dynamics model into the inference that controlled the variance of the prior being used to infer edge locations based on previous observations. FIG. 5 illustrates the multiple prior dependencies of the hierarchical Laplacian scale mixture model described in Eq. (7,8,9) using a graphical model.

To build dynamics into the model, it was observed that the Gamma distribution's scale variable θ_(k)[i] controlled its expected value (i.e., E[γ_(k)[i]=αθ_(k)[i]). The inventors then designed a dynamic filtering approach to the problem of interest by using a dynamics model on the edge-pixels that set the individual variances θ_(k)[i]'s according to predictions from the dynamics model g_(k)(·):

${{\theta_{k}\lbrack i\rbrack} = \frac{\xi}{{{{g_{k}\left( t_{k - 1} \right)}\lbrack i\rbrack}} + \eta}},$ where ξ is a positive constant and η is a small constant that prevents division by zero. To illustrate the operation of this model, a strong edge-pixel in a previous frame (i.e., a large value of t_(k−1)[i]) set a small value of θ_(k)[i] (and respectively a small expected value of γ_(k)[i]), in turn making the Laplacian's variance large (i.e., Var[t_(k)[i]]=2/(γ₀γ_(k)[i])²). A large Laplacian variance implied a higher likelihood that the edge-pixel in the current frame was active (in contrast to the reverse situation where a weak edge pixel would result in a small Laplacian variance at the next time step). Therefore, this approach propagated second-order statistics (similar to classic Kalman filtering for Gaussian models) through the hyperpriors γ_(k) using dynamic information via the evolution function g_(k)(·) at each time-step. One option for g_(k)(·) was a convolution against a Gaussian kernel (with its σ proportional to expected motion variation), which expresses a confidence neighborhood of edge locations based on previous edge locations [47]. As with any tracking algorithm, the tracking quality depended on the accuracy of the dynamics model and including better models (e.g., more accurate motion speeds, motion direction information based on pipette movement, etc.) would improve the performance of any approach. With a fixed dynamics function, for each frame the algorithm took a re-weighting approach where multiple iterations are used to adaptively refine the estimates at each model stage (illustrated for a simulated patch in FIG. 6).

The final optimization followed from taking the MAP estimate for Eq. (7,8,9) and applying the EM approach to iteratively update the weights. In some cases, the maximization step is given as a convex formulation

$\begin{matrix} \begin{matrix} {{\hat{x}}_{k}^{(t)} = {\arg\;{\min\limits_{x \geq 0}{- {\log\left\lbrack {p\left( x \middle| \gamma_{k}^{(t)} \right)} \right\rbrack}}}}} \\ {= {{\arg\;{\min\limits_{x \geq 0}{\frac{1}{2}{{{F_{k}y_{k}} - {Dx}}}_{2}^{2}}}} +}} \\ {\gamma_{0}{\sum\limits_{i = 1}^{N}{{\gamma_{k}^{(t)}\lbrack i\rbrack} \cdot {{{T_{i}x}}_{2}.}}}} \end{matrix} & (10) \end{matrix}$ In other words, {circumflex over (x)}_(k) ^((t)) is the value of x for a given iteration (t) of a given image k (e.g., frame) that minimizes the cost function: 1/2∥F_(k)y_(k)−D_(x)∥₂ ²+γ₀ ^((t))Σ_(i=1) ^(N)γ_(k) ^((t))[i]·∥T_(i)x∥₂. In light of the present disclosure, of ordinary skill will recognize that the first portion of equation 10 (½∥F_(k)y_(k)−Dx∥₂ ²) represents the least mean square error of the prediction x^((t)) from the true image, while the second portion of Equation 10 (γ₀ ^((t))Σ_(i=1) ^(N)γ_(k) ^((t))[i]·∥T_(i)x∥₂) represents the total derivative value for the image for a given prediction x^((t)). The second portion describes how “connected” the predicted edges are in a statistical sense. The cost function balances the predicted error and the “connectedness” of the prediction.

DIC deconvolution can be particularly sensitive to uneven (i.e., non-matching) boundaries. Hence, the implementation of the matrix operator D, though application dependent, should be treated carefully. In some embodiments, a discrete convolutional matrix implementation that handled non-matching boundary could cause memory issues when N is large since D scales quadratically in size (though it could be mitigated using sparse matrices). Alternatively, in some embodiments, an FFT/IFFT surrogate implementation implies circular boundary conditions that need to be explicitly taken care of (e.g., via zero-padding). The expectation step may be using the conjugacy of the Gamma and Laplace distributions, admitting the closed-form solution

$\begin{matrix} \begin{matrix} {{\gamma_{k}^{({t + 1})}\lbrack i\rbrack} = {{\mathbb{E}}_{p{({\gamma|{{\hat{t}}_{k}^{(t)}{\lbrack i\rbrack}}})}}\lbrack\gamma\rbrack}} \\ {{= \frac{\kappa + 1}{{\kappa \cdot {{{\hat{t}}_{k}^{(t)}\lbrack i\rbrack}}} + {{{g_{k}\left( {\hat{t}}_{k - 1} \right)}\lbrack i\rbrack}} + \eta}},} \end{matrix} & (11) \end{matrix}$ where the Expectation Maximization (EM) iteration number is denoted by superscript t, t_(k) ^((t))[i]=∥T_(i)x_(k) ^((t))∥₂ is the estimate of the edge at iterate t, t_(k−1)[i]=∥T_(i)x_(k−1)∥₂ is the estimate of the edge at the previous time-step, γ₀ is the positive constant that controlled the weight of edge-sparsity against reconstruction fidelity, and κ is the positive constant that controls the weight of the current observation against the dynamics prior. The Gaussian convolution implemented by g_(k)(·) effectively “smeared” the previous time-step's estimation of edges to form the current prior, accounting for uncertainty due to cell movement over time. In other words, g_(k)(·) ties the edge prediction of a current image to the edge prediction of the previous image in the sequence. The EM algorithm was initialized by setting all weights to 1 (i.e., γ_(k) ⁽⁰⁾=1) and solving Eq. 10, which is simply (non-weighted) TV-regularized least squares. The reweighting iterations were terminated upon reaching some convergence criteria (e.g., ∥x^((t))−x^((t−1))∥₂/∥x^((t))∥₂<ε, or the cost function value for {circumflex over (x)}_(k) ^((t)) being less than a certain threshold (which may work as a stand-in for fit) or after a fixed number of reweights. C. Object Removal via Inpainting

When an object (e.g., a pipette) draws near to a cell for interaction (e.g., patching), the object in the image patch can cause significant errors in the deconvolution process. Accordingly, in some cases, the PF+RWTV-DF algorithm may be modified to accommodate objects within the image. For example, an inpainting approach may mask away the object's pixels and inferred the missing pixels according to the same inverse process used for deconvolution. To begin, the object location may be tracked in the image with a similar template matching process as described above (which could be improved with positional information from an actuator if available). Simultaneously, an associated object mask (obtained either via automatic segmentation or manually drawn) was aligned and overlaid on top the cell image patch using the updated pipette locations. This object mask overlay may take the form of a masking matrix M ∈ {0,1}^(M×N) whose rows are a subset of the rows of an identity matrix, and whose subset is defined by pixel indices outside the pipette region. The original filtered observation F_(k)y ∈

^(N) is reduced to M F_(k)y ∈

^(M) (with M≤N) while the convolution operator becomes M D. The inpainting version of Eq. (10) is

$\begin{matrix} {{\hat{x}}_{k}^{(t)} = {{\arg\;{\min\limits_{x \geq 0}{\frac{1}{2}{{{{MF}_{k}y_{k}} - {MDx}}}_{2}^{2}}}} + {\gamma_{0}{\sum\limits_{i = 1}^{N}{{\gamma_{k}^{(t)}\lbrack i\rbrack}{{{T_{i}x}}_{2}.}}}}}} & (12) \end{matrix}$

Pixels are removed in the object region from the data used in the deconvolution, but the algorithm may infer pixel values consistent with the statistical model used for regularization.

D. Reweighting Modification

In some implementations, solving the deconvolution problem (i.e., Equations 10 and 11 described above) at the current video frame in real-time may be computationally expensive. In implementing the described algorithm, the main computational bottleneck lies in solving the expensive optimization of Equation 10. In some implementations, Alternating Directions Method of Multipliers (ADMM) may be used to solve Equation 10. As will be understood by one of ordinary skill, ADMM framework is itself also iterative in nature, where the numerical precision of the method is proportional to the number of iterations the solver carries out. For very high precision, the number of iterations would easily run into the thousands. Thus, solving Equation 10 with high precision (e.g., before reweighting in Equation 11) may take significant time, and request significant and computing power. However, in some implementations, RWTV-DF is merged with ADMM iterations under a single solver “umbrella”. By drastically reducing the time spent on producing high precision solutions in each iteration of Equation 10, and performing more rounds of reweighting, high-precision may be had for a final edge estimation for a given frame without requiring high precision estimations in each iteration.

FIG. 18 illustrates example edge determinations for a given frame for different iterations of ADMM between reweighing T. Meanwhile, FIG. 19 illustrates aggregated statistics of RWTV-ADMM for different iterations of ADMM between reweighing T according to an example implementation. Thus, as can be seen, certain implementations may increase edge determination speed by utilizing lower-fidelity while selective increasing iteration times.

Results

A. Experimental Conditions

The performance of an implementation of the invented algorithm was evaluated by using a cell simulator that generates synthetic DIC imagery of rodent neurons in brain slices. Herein is shown the simulation framework and its realism is demonstrated by comparisons against data.

Most cell simulators can be described as having three distinct stages: cell-shape generation, optical imaging, and noise generation. The simulation framework implemented for this method used these same three stages (shown in FIG. 7), adapting general approaches used in the literature for each stage so that the simulated data reflects the statistics of the DIC microscopy images for in vitro brain slice electrophysiology. In the first stage, a synthetic cell-shape was generated and embedded into the pixel-space as an ideal OPL image (i.e., the ground truth). In the second stage, the OPL image was transformed using a convolution against an idealized point spread function that approximately described the DIC microscope's optics. Lastly, interference from static components (e.g., organic material) and dynamic noise components (e.g., the image acquisition system) are generated and incorporated into the image during the third stage. Herein, the inventors have used existing general approaches to build and validate the model components in the simulator using real DIC imagery of in vitro brain slices from adult (P50-P180) mice as described in [49]. This simulator is unique in that it is tailored to simulate this type of cells. Full implementation details for this simulator are discussed below.

To evaluate the realism of synthetically generated cell-shapes, the inventors compared several of their shape features to actual hand-drawn cell shapes from rodent brain slice imagery using four dimensionless shape features:

-   -   1) Aspect Ratio was defined as the ratio of minor axis lengths         to major axis lengths. The major/minor axis was determined from         the best fit ellipsoid of the binary image.     -   2) Form factor (sometimes known as circularity) was defined as         the degree to which the particle is similar to a circle (taking         into consideration the smoothness of the perimeter [50]),         defined as

$\frac{4\pi\; A}{P^{2}},$

-   -    where A is area and P is the perimeter.     -   (3) Convexity was a measurement of the particle edge roughness,         defined as

$\frac{P_{cvx}}{P}$

-   -    where P_(cvx) is the convex hull perimeter and P is the actual         perimeter.     -   4) Solidity was the measurement of the overall concavity of a         particle, defined as

$\frac{A}{A_{cvx}},$

-   -    where A_(cvx) is the convex hull area and A is the image area         [51].

Using 50 shape-coordinates per cell the inventors generated 115 synthetic cells. The quartile-quartile plots in FIG. 8 showed that all four features are similarly distributed, demonstrating that the simulation renders realistic cell shapes for rodent in vitro brain slices.

Several simulation images were generated in FIG. 9 for visual comparison against actual cell images. The following user-defined parameters (as defined in Table I) were used: image size was 60×60, cell-rotation (θ_(rot)) was randomized, cell-scaling defined as factor of image width was γ_(scale)=0.8, DIC EPSF parameters were {θ_(d)=225°, σ_(d)=0.5}, dynamic noise parameters were {Ag=0.98, σ_(g)=0.018, A_(p)=20.6, λ_(p)=10⁻¹⁰}, and SNR_(χ)=−1 dB. Cell shapes were randomly generated based on learned real cell-shapes, a lighting bias was taken randomly from actual image patches, and organic noise was generated using a RAPSD curve learned from real DIC microscopy images. In general, the synthetic and actual cells were qualitatively similar in cell shapes and noise textures.

TABLE I User-Defined Simulator Properties Parameter Description M Image size (i.e., M × M pixel-image) θ_(rot) Rotation angle of cell-shape γ_(scale) Scaling factor of cell-shape within image p Persistence of OPL surface texture {σ_(d), θ_(d)} DIC imaging function parameters (Eq. (1)) {A_(g), σ_(g)} Dynamic noise Gaussian parameters (Eq. (15)) {A_(p), λ_(p)} Dynamic noise Poisson parameters (Eq. (15)) χ SNR (in dB) of final image (Eq. 16) B. Segmentation of Synthetic Data

The inventors tested an implementation of the PF+RWTV-DF algorithm on synthetic cell data and compared its performance against the state-of-the-art deconvolution algorithms such as least-squares regularized by l1 and TV (L1+TV) [20], least-square regularized by l1 and Laplacian Tikhonov (L1+TIK) [20], and least-square by regularized re-weighted l1, weighted Laplacian Tikhonov, and weighted dynamic filtering (RWL1+WTik+WDF) [30]. The deconvolution from each algorithm is then segmented using a global threshold (using Otsu's method [45]) to produce a binary image mask for algorithmic evaluation.

For evaluation, the inventors employed three boundary metrics that captured errors relevant to the process of patch clamping. The metrics Average Boundary Error (ABE), Maximum Boundary Error (MBE), and Variance of Boundary Errors (VBE) measured the (average, maximum, and variance of) distance errors between the approximated cell boundary and the actual cell boundary around the entire membrane of the cell at each video frame. Specifically, these metrics captured the statistics of the distance errors between the actual and estimated cell boundaries as the pipette tip approaches the cell membrane in a straight path (directed towards the true centroid).

To compute these metrics, the inventors first discretized potential pipette paths towards the true centroid using a set of lines {l_(a)}, defined as lines that start at the true centroid and that infinitely extend through each point p_(a) in the set of ground truth contour pixels {A}. Next, traveling along each l_(a) toward the centroid we found the intersecting point in the set of estimated contour pixels {B}, defined as p_(a,B)=arg min_(p) _(b) _(∈B)∥p_(b)−p_(l)∥₂s.t. p_(l)∈l_(a), where p_(l) are points on the line l_(a). In other words, the inventors found the points that the algorithm would identify as the membrane location during every hypothetical approach direction of the pipette. The ∥p_(b)−p_(l)∥₂ in the objective considers only orthogonal projections of p_(b) unto the line l_(a) (since it is a minimization), and it searches over all of B to find the p_(b) whose orthogonal projection distance is minimal. Note that that due to the contour discretization, pa,B does not lie exactly along la but rather close to it on some p_(b) ∈ B. With each discretized boundary error expressed as ε(a, B)=∥p_(a,B)−p_(a)∥₂, the metrics are then defined as:

${{ABE}\left( {A,B} \right)} = {\frac{1}{{A}_{0}}{\sum\limits_{a \in A}{ɛ\left( {a,B} \right)}}}$ ${{MBE}\left( {A,B} \right)} = {\max\limits_{a \in A}\;{ɛ\left( {a,B} \right)}}$ ${{VBE}\left( {A,B} \right)} = {\frac{1}{{A}_{0} - 1}{\sum\limits_{a \in A}{\left( {{ɛ\left( {a,B} \right)} - {{ABE}\left( {A,B} \right)}} \right)^{2}.}}}$ FIG. 10 illustrates the terms involved in these error metric computations.

The inventors generated 100 videos of synthetic cell patches (each video contains 64×64 pixels×100 frames) using the proposed cell simulator with DIC EPSF parameters σ_(d)=0.5 and θ_(d)=225° (assumed to be known either by visual inspection (to accuracy of ±15°) or more accurately by using a calibration bead [22]). By physically relating real cells to simulated cells, the inventors determined the relationship between physical length and pixels to be approximately 3.75 pixels per 1.0 μm.

For the algorithms L1+TV, L1+Tik, and RWL1+WTik+WDF, the parameters for sparsity (β) and smoothness (γ) were tuned via exhaustive parameter sweep on the first frame of the video (to find the closest reconstruction/deconvolution by the l2 least squares sense). Specifically, the sweep was conducted over 10 logarithmically spaced values in the given ranges: L1+TV searched over [10⁻³, 10⁻⁹] for β and [10⁻¹, 10⁻⁵] for γ, L1+Tik searched over [10⁻³, 10⁻⁹] for β and [10⁻¹, 10⁻⁷] for γ, and RWL1+WTik+WDF searched over [10⁻³, 10⁻⁹] for β and [10⁻¹, 10⁻⁵] for γ. L1+TiK (the non-reweighted version) was used in all experiments because it was experimentally found to be better performing compared to the reweighted version; reweighting over-induced sparsity of pixels, which is not advantageous to segmentation in this particular application. For RWL1+WTik+WDF, the dynamics parameter was set to be δ=1.0×10⁻³, with a maximum of 80 reweighting steps (where convergence is fulfilled before each reweighting). For PF+RWTV-DF (Eq. (10, 11)), the inventors fixed γ₀=3.0×10⁻⁴, κ=5, with 4 reweighting steps (where convergence is fulfilled before each reweighting). The programs specified by L1+TV, RWL1+WTik+WDF, and PF+RWTV-DF were solved using CVX [52], [53], while LI+Tik was solved using TFOCS [54].

FIG. 11 reflects statistics of the respective algorithms from each of the 100 frames from the 100 video trials. The height of each bar refers to the average of ABE/MBENBE while the error bars refer to ±1 standard error of the ABE/MBENBE over the 100 video trials. PF+RWTV-DF was the best performing algorithm in the three metrics, and there was a significant difference (p≤0.001) between PF+RWTV-DF and the other algorithms for all metrics. Notably, PF+RWTV-DF resulted in boundary tracking errors on the order of 1-2 μm, which is comparable to the error in mechanical pipette actuators.

The implemented edge reweighing strategy is adaptive by design, making it very attractive in practice because it requires minimal parameter fine-tuning. The algorithm's performance was responsive to the smoothness parameter (effective range being γ∈ [2.0×10⁻⁴, 4.0×10⁻⁴]) and the dynamics parameter (effective range being κ∈ [10⁰, 10²]), yet not over-sensitive: the invented algorithm's superior results were from fixed parameters (γ, κ) across all trials, while other algorithms required exhaustive two-parameter sweeps (β, γ) for each synthetic video trial.

FIG. 12 shows one representative trial (Trial #4) in the time-series to observe the qualitative differences between the algorithms. It was observed that the PF+RWTV-DF reconstruction has a fairly flat magnitude (for pixel values within the cell) compared to the other reconstructions. The proposed algorithm's inherent segmentation capability under such high-interference synthetic data is apparent from these results. Although PF+RWTV-DF reconstruction lost some cell details (i.e., in an l2 reconstruction sense), the reduction in surrounding interference served to improve the boundary identification at the segmentation stage. On the other hand, the other algorithms produced reconstructions that contained significant surrounding interference, resulting in distorted edges in their subsequent segmentations (that may require further image processing to remove).

C. Segmentation of Real Data

In addition to the synthetic data where ground truth was known, the inventors also tested the algorithms on in vitro DIC microscopy imagery of rodent brain slices from the setup described in [49]. For each algorithm, a parameter search was performed using a brute-force search to find the parameters that best segmented the cell by means of visual judgement. The DIC EPSF was estimated visually to be σ_(d)=0.5, θ_(d)=225°.

In FIG. 13A-13C, three particularly challenging cell samples were selected with respect to the amount of observable interference around and within the cell. A fixed global threshold was applied to each patch for segmentation using Otsu's method [45]. The first example (FIG. 13A, from the top) demonstrated that reconstructions of other algorithms (compared to the proposed algorithm) were characteristically not piecewise smooth. Therefore, even in a case of moderate difficulty such as this one, these algorithms produce images with rounded edges which are not ideal for segmentation. The second example (FIG. 13B) illustrated difficulty in segmenting cells with significant interference along the cell's edges, around the outside of the cell, and within the body of the cell. In this case, only the proposed algorithm is able to produce a clean segmentation, especially along the cell's edges. Moreover, other algorithms reproduce the heavy interference scattered around the outside of the cell and this requires subsequent image processing to remove. The third example (FIG. 13C) was a very difficult case where interference occurs not only as distorted boundaries, but also as a close neighboring cell. All other algorithms visibly performed poorly while the proposed algorithm remained fairly consistent in its performance.

In FIG. 14, snapshots from a video of a cell undergoing patch clamping was compared with and without the proposed pipette removal method. The pipette (and its respective mask) was tracked using a template matching algorithm via a user-selected template of the pipette; more details are described in [44]. In FIG. 14A, the pipette did not cause interference when it was relatively far away from the cell. As the pipette approached the cell in FIG. 14B, interference began to enter the deconvolution when inpainting was not applied. Without inpainting, an obfuscation between the pipette and the cell was observed in the deconvolution even when the pipette was not overlapping with the cell. In FIG. 14C, the pipette was seen to be overlapping the cell image. Without inpainting, this overlap caused such severe interference that attempting a pipette removal at the segmentation stage is clearly non-trivial. With inpainting, the deconvolution was shown to effectively suppress the interfering pipette in all three snapshots.

Conclusion

Herein is described a new deconvolution algorithm to locate cell boundaries with high precision in DIC microscopy images of brain slices. In summary, some of the technical contributions of this algorithm are: (1) a pre-filtering step that is a computationally cheap and effective way of removing heavy organic interference with spectral characteristics, (2) a dynamical l1 reweighing approach for the propagation of second-order edge statistics in online DIC cell segmentation, and (3) an inpainting approach for pipette removal that is possible with little modification due to the inherently flexible framework of the algorithm. To quantitatively validate the performance of segmentation algorithms, this Example also describes the novel adaptation of cell simulation techniques to the specific data statistics of DIC microscopy imagery of brain slices in a publicly available MATLAB toolbox.

The proposed algorithm achieves state-of-the-art performance in tracking the boundary locations of cells, with the average and maximum boundary errors achieving the desired tolerances (i.e., 1-2 μm) driven by the accuracy of actuators used for automatic pipette movement. These results led to the conclusion that accurate visual guidance can be possible for automated patch clamp systems, resulting in a significant step toward high-throughput brain slice electrophysiology. A possible shortfall of the proposed algorithm arises from the implicit assumption that dynamics are spatially limited. In order for dynamics to positively contribute to the deconvolution process, edges in the current frame should fall within the vicinity of the previous frame's edges; specifically, it should be bounded by the support of the prediction kernel as described by Eq. (11). Improvements to the invented method could include developing a real-time numerical implementation of this algorithm using parallelization methods such as alternating direction methods of multipliers (ADMM) similar to work found in [55] and [56], exploring the inclusion of shape-regularizers [57]-[59] into the optimization, investigating alternative methods that incorporate dynamics in a fashion that is not spatially-limiting, and characterizing dynamical functions that take into account physical models of motion in the system (e.g., motion induced by the pipette, fluid dynamics, cell deformation physics).

Simulation Framework

A. Simulation Stage 1: Cell Shape Generation

The cell-shape is unique to different applications and can play a significant role in algorithm development, necessitating customization in cell simulations [35], [60]. Extensive work on generic shape representation in [60] demonstrated that applying principal components analysis (PCA) on cell-shape outlines can be an excellent strategy for reconstructing cell shapes. Herein, the inventors applied a similar approach as [35] to generate synthetic cell-shapes using PCA and multivariate kernel density estimation sampling on subsampled cell contours. For shape examples, the inventors used hand drawn masks of neurons from DIC microscopy images of rodent brain slices.

Example cell-shapes were collected such that K coordinates were obtained in clockwise continuous fashion (around the contour), beginning at the north-most point. These points were centered such that the centroid is at the origin. The (x, y) coordinates were concatenated into an

^(d) vector x _(i)=(x ₁ , . . . , x _(K) , y ₁ , . . . , y _(K))^(T), where d=2K. This vector was then normalized via {circumflex over (x)}_(i)=x_(i)/∥x_(i)∥₂. All N normalized examples were gathered into the following matrix X=({circumflex over (x)} ₁ , . . . ,{circumflex over (x)} _(N)).

Eigen-decomposition was performed on the data covariance matrix formed as S=XX^(T)=V∧V^(T). Cell-shapes may thus be expressed with the coefficient vector b_(i) and the relationship given by x _(i) =Vb _(i) ⇔b _(i) =V ^(T) x _(i).  (13)

Since PCA guarantees that cov(b_(i), b_(j))=0, ∀i≠j, kernel density estimation was performed individually on each of the coefficients to estimate its underlying distributions. This allows users to randomly sample from these distributions to produce a synthetically generated coefficient vector, {tilde over (b)}. The cell-shape may then be trivially converted into coordinates using the relationship given in Eq. (13). A rotation (θ_(rot)) and scaling (γ_(scale)) are added to the cell-shapes where necessary. FIG. 15A-15B show a sampling of synthetic and actual cell-shapes extracted from the data.

1) Textured OPL Pixel-Space Embedding: The previously generated cell-shape was embedded into the pixel space f_(x,y) by a texture generation method similar to methods found in other fluorescence microscopy simulators [61], [62]. In this stage, the cell-shape was embedded into the pixel space with the generation of a textured OPL image. Perlin noise [63] is a well-established method for generating synthetic cell textures in fluorescent microscopy [61], [62], and the inventors applied a similar concept because it generated realistic looking cell textures.

First, a binary mask, m(x, y), was generated using the cell-shape's coordinates as polygon vertices and cast into an M×M image. Next, a textured image, t(x, y) was generated by frequency synthesis; a 2-D filter with a 1/f^(p) frequency spectra was applied to white Gaussian noise, where p is a persistence term which controls the texture's heterogeneity. t(x, y) is rescaled such that {circumflex over (t)}(x,y) ∈ [0, 1]. Finally, the OPL image is constructed by f(x,y)=(m(x,y)*h(x,y))·(m(x,y)·{circumflex over (t)}(x,y)), where * signifies 2D convolution, and h(x, y) is a 2-D filter (e.g., a circular pillbox averaging filter) that rounds the edges of the OPL image. An example surface texture is simulated and shown in FIG. 7B. B. Simulation Stage 2: Optical Imaging

Microscopy optics was modeled here using two linear components: an effective point spread function (EPSF) and a lighting bias. DIC microscopy exploits the phase differential of the specimen to derive the edge representations of microscopy objects. The EPSF is approximated as a convolution of the OPL image f (x, y) against the steerable first-derivative of Gaussian kernel, in Eq. (1).

Nonuniform lighting of a microscope often causes a pronounced lighting bias in the image. As presented in [20] and [64], a linear approximation of quadratic coefficients sufficiently expresses such a bias: b(x,y)=p ₀ +p ₁ x+p ₂ y+p ₃ x ² +p ₄ xy+p ₅ y ².  (14) An example noiseless simulated image with the optical imaging model (including EPSF convolution and lighting bias) is shown in FIG. 7C. Polynomials p₀, . . . , p₅ are estimated from a randomly extracted patch from an actual DIC image using a least-squares framework detailed in [20]. C. Simulation Stage 3: Noise Generation

-   1) Synthetic Noise Generation Framework: Noise in a video frame may     be linearly decomposed into organic and sensor components:     n _(k)(x,y)=n ^(orgānic)(x,y)+n _(k) ^(sensor)(x,y),     with k denoting the frame index in time. The inventors defined     n^(organic) (x, y) as the components comprising of organic     contributions in the specimen (e.g., cellular matter, fluids) that     remain static frame-to-frame, while n_(k) ^(sensor) (x, y) refers to     noise from the CCD that is iid across every pixel and frame. For the     purpose of statistical estimation, the inventors selected sequences     of image frames {y_(k)(x, y)}_(k=1, . . . , K) that represented     noise only (i.e., no target cell) with no tissue motion from pipette     insertion. The inventors estimated the organic noise component by     averaging a series of image frames (to reduce sensor noise):

${{n^{organic}\left( {x,y} \right)} \approx {\overset{\_}{y}\left( {x,y} \right)}} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}{{y_{k}\left( {x,y} \right)}.}}}$

Similarly, a sensor noise sample may be estimated by subtracting the frame-average from the individual frame: n _(k) ^(sensor)(x,y)≈y _(k)(x,y)− y (x,y).

-   2) Organic Noise: The inventors employed a spectral analysis     framework to model and generate realistic looking interference     caused by organic tissue. The inventors defined the radially     averaged power spectral density (RAPSD), P(f), as an averaging of     the power spectral density (PSD) magnitudes along a concentric ring     (whose radius is proportional to frequency, denoted by (f) on a     DC-centered spatial PSD Fourier plot. The RAPSD of random noise     images reveal spectral characteristics shown in FIG. 16D. Phase     information is simulated by randomly sampling from a uniform     distribution Φ (m, n)˜Uniform([0, 2π]), with m, n representing the     spatial coordinates in the DC-centered Fourier domain, while the     magnitude information is composed as a mean spectra P(f) from RAPSD     of example image patches {P_(k)}_(k=1, . . . K) as

${\overset{\_}{P}(f)} = {\frac{\sqrt{2}}{K}{\sum\limits_{k = 1}^{K}{{P_{k}(f)}.}}}$ The organic noise spectrum is thus described by its magnitude and phase components as {tilde over (S)}(m,n)=| P (√{square root over (m ² +n ²))}|exp(j·Φ(m,n)). An inverse spatial Fourier transform on the organic noise spectrum yields a synthetic organic noise image: ñ ^(organic)(x,y)=F⁻¹ {{tilde over (S)}(m,n)}. An example organic noise image patch ñ^(organic) (x, y) (shown in FIG. 16A) exhibits visual similarities with a patch of organic noise from an actual DIC image (shown in FIG. 16B). Additionally, similarities were observed in pixel distributions between synthetic organic noise and actual organic noise, qualitatively as shown in FIG. 16C, as well as quantitatively via a Kolmogorov-Smirnov two-sample goodness-of-fit test at the 5% significance level (after normalization by their respective sample standard-deviations).

-   3) Sensor Noise: The CCD sensor contributes a mixture of Poisson     noise and zero-mean white-Gaussian noise [62], [64]. For modeling     simplicity, the inventors assumed that the sensor's individual     pixels are uncorrelated in time and space, and generated using     n _(k) ^(sensor)(x,y)=A _(g) ·n _(g) +A _(p) ·n _(p),  (15)     where n_(g)˜Normal(0, σ_(g) ²) and n_(p)˜Poisson(λ_(p)) are randomly     generated intensity values, {Ag, Ap} are amplitude parameters, and     {σ_(g),λ_(p)} are the Gaussian's standard deviation and the     Poisson's mean parameters respectively.     D. Image and Video Synthesis     1) Image Synthesis: Each simulation frame is generated as a linear     combination of the various synthesized components

$\begin{matrix} {{{y\left( {x,y} \right)} = {{\left\lbrack {10^{\chi/10}\frac{{{n\left( {x,y} \right)}}_{F}}{{{g\left( {x,y} \right)}}_{F}}} \right\rbrack \cdot {g\left( {x,y} \right)}} + {n\left( {x,y} \right)} + {b\left( {x,y} \right)}}},} & (16) \end{matrix}$ where χ is a user-defined signal-to-noise ratio (in dB), and where ∥⋅∥F is the Frobenius norm. Table I summarizes the user-defined parameters of this simulator. 2) Video Synthesis: During the patch clamp process, pipette motion causes the cells to undergo overall translation (e.g., moving from left to right with respect to the frame), and some sequence of dilation and contraction. Videos of K image frames are generated to simulate motion of the cell (rather than the pipette itself) by evolving a single textured OPL pixel-space embedding image over time using a series of geometric transformations. Specifically, we simulate a dilation/contraction using MATLAB's barrel transformation function [65] and apply geometric translation along a random linear path through the center of the image with a parabolic velocity profile (e.g., an acceleration followed by a deceleration). These transformations produced a set of frames {f_(k)(x, y)}_(k=1,2), . . . which are convolved in 2D using Eq. (1) and synthesized using Eq. (16) to generate a set of time-varying observations {y_(k)(x, y)}_(k=1,2), . . . comparable to a video sequence of DIC imagery from a patch clamp experiment. Example snapshots from a synthetic video is shown in FIG. 17. Example Environment and Computer Architecture

FIG. 20 illustrates an example environment 2000 in which certain aspects of the present disclosure may be implemented. The environment 2000 includes a process system 2005 and a tissue sample 2095. One of ordinary skill will recognize that this is merely an example environment, and aspects of the present disclosure may be applied outside of the presently discussed context. The process system 2005 may include a process controller 2010, a DIC microscope 2020, a cell identification and tracking processor 2030 (ID processor 2030), and an actuator 2040. An example computer architecture that may implement one or more aspects of the process controller 2010, DIC microscope 2020, cell identification and tracking processor 2030, and actuator 2040 are described below with reference to FIG. 21.

Process system 2005 is configured to perform a process on tissue sample 2095. For example, process system 2005 may be configured to perform automatic cell patch clamp electrophysiology on the tissue sample 2095 (e.g., brain tissue). However, one of ordinary skill will recognize that this is merely an example.

Process controller 2010 controls the behavior of the remaining components of process system 2005. DIC microscope 2020 may capture images of the tissue sample 2095 using DIC microscopy. One of ordinary skill will recognize that this is merely an example, and additional and/or alternative imaging techniques may be utilized. The DIC microscope 2020 may provide images of the tissue sample to the process controller 2010 (e.g., in real-time). The process controller 2010 provides the images to ID processor 2030.

ID processor 2030 may be configured to identify a boundary of a cell of the tissue sample within the images captured by DIC microscope 2020. As non-limiting examples, ID processor 2030 may perform patch tracking, deconvolution, and segmentation on the images to identify the cell boundary, for instance, as described above in greater detail. ID processor 2030 may provide the boundary information to the process controller 2010.

Process controller 2010 may then control actuator 2040 to move an instrument to coordinates corresponding to the cell boundary. In some cases, process controller 2010 may convert the image location information from ID processor 2030 to coordinates corresponding to the tissue sample.

Although process controller 2010, DIC microscope 2020, cell identification and tracking processor 2030, and actuator 2040 are depicted as separate, one of ordinary skill will recognize that various features and configurations of the process controller 2010, DIC microscope 2020, cell identification and tracking processor 2030, and actuator 2040 may be combined into one or more physical or logical devices.

FIG. 21 illustrates an example computing device architecture than can implement one or more aspects of the process system 2005, process controller 2010, DIC microscope 2020, cell identification and tracking processor 2030, and actuator 2040, and a method according to the present disclosure. In some embodiments, process controller 2010, DIC microscope 2020, cell identification and tracking processor 2030, and actuator 2040 may have fewer, alternative, or additional components as that illustrated in FIG. 21.

The computing device architecture 2100 of FIG. 21 includes a central processing unit (CPU) 2102, where computer instructions are processed, and a display interface 2104 that acts as a communication interface and provides functions for rendering video, graphics, images, and texts on the display. In certain example implementations of the disclosed technology, the display interface 2104 may be directly connected to a local display, such as a touch-screen display associated with a mobile computing device. In another example implementation, the display interface 2104 may be configured for providing data, images, and other information for an external/remote display 2150 that is not necessarily physically connected to the mobile computing device. For example, a desktop monitor may be used for mirroring graphics and other information that is presented on a mobile computing device. In certain example implementations, the display interface 2104 may wirelessly communicate, for example, via a Wi-Fi channel or other available network connection interface 2112 to the external/remote display 2150.

In an example implementation, the network connection interface 2112 may be configured as a communication interface and may provide functions for digital virtual assistant using voice, rendering video, graphics, images, text, other information, or any combination thereof on the display. In one example, a communication interface may include a microphone, camera, serial port, a parallel port, a general-purpose input and output (GPIO) port, a game port, a universal serial bus (USB), a micro-USB port, a high definition multimedia (HDMI) port, a video port, an audio port, a Bluetooth port, a near-field communication (NFC) port, another like communication interface, or any combination thereof. In one example, the display interface 2104 may be operatively coupled to a local display, such as a touch-screen display associated with a mobile device or voice enabled device. In another example, the display interface 2104 may be configured to provide video, graphics, images, text, other information, or any combination thereof for an external/remote display 2150 that is not necessarily connected to the mobile computing device. In one example, a desktop monitor may be used for mirroring or extending graphical information that may be presented on a mobile device. In another example, the display interface 2104 may wirelessly communicate, for example, via the network connection interface 2112 such as a Wi-Fi transceiver to the external/remote display 2150.

The computing device architecture 2100 may include a keyboard interface 2106 that provides a communication interface to a keyboard. In one example implementation, the computing device architecture 2100 may include a presence sensitive input interface 2108 for connecting to a presence sensitive display 2107. According to certain example implementations of the disclosed technology, the presence sensitive input interface 2108 may provide a communication interface to various devices such as a pointing device, a touch screen, a depth camera, microphone, etc. which may or may not be associated with a display.

The computing device architecture 2100 may be configured to use an input device via one or more of input/output interfaces (for example, the keyboard interface 2106, the display interface 2104, the presence sensitive input interface 2108, network connection interface 2112, camera interface 2114, sound interface 2116, etc.) to allow a user to capture information into the computing device architecture 2100. The input device may include a mouse, a trackball, a directional pad, a track pad, a touch-verified track pad, a presence-sensitive track pad, a presence-sensitive display, a scroll wheel, a digital camera, a digital video camera, a web camera, a microphone, a sensor, a smartcard, and the like. Additionally, the input device may be integrated with the computing device architecture 2100 or may be a separate device. For example, the input device may be an accelerometer, a magnetometer, a digital camera, a microphone, and an optical sensor.

Example implementations of the computing device architecture 2100 may include an antenna interface 2110 that provides a communication interface to an antenna; a network connection interface 2112 that provides a communication interface to a network. As mentioned above, the display interface 2104 may be in communication with the network connection interface 2112, for example, to provide information for display on a remote display that is not directly connected or attached to the system. In certain implementations, camera interface 2114 acts as a communication interface and provides functions for capturing digital images from a camera. In certain implementations, a sound interface 2116 is provided as a communication interface for converting sound into electrical signals using a microphone and for converting electrical signals into sound using a speaker. In certain implementations, a sound interface 2116 is utilized to capture voice inputs for consumption by of other components connected to the BUS 2134. According to example implementations, a random-access memory (RAM) 2118 is provided, where computer instructions and data may be stored in a volatile memory device for processing by the CPU 2102.

According to an example implementation, the computing device architecture 2100 includes a read-only memory (ROM) 2120 where invariant low-level system code or data for basic system functions such as basic input and output (I/O), startup, or reception of keystrokes from a keyboard are stored in a non-volatile memory device. According to an example implementation, the computing device architecture 2100 includes a storage medium 2122 or other suitable type of memory (e.g. such as RAM, ROM, programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic disks, optical disks, floppy disks, hard disks, removable cartridges, flash drives), where the files include an operating system 2124, application programs 2126 (including, for example, a web browser application, a widget or gadget engine, and or other applications, as necessary) and data files 2128 are stored. According to an example implementation, the computing device architecture 2100 includes a power source 2130 that provides an appropriate alternating current (AC) or direct current (DC) to power components.

According to an example implementation, the computing device architecture 2100 includes a telephony subsystem 2132 that allows the computing device to transmit and receive sound over a telephone network. The constituent devices and the CPU 2102 communicate with each other over a bus 2134.

According to an example implementation, the CPU 2102 has appropriate structure to be a computer processor. In one arrangement, the CPU 2102 may include more than one processing unit. The RAM 2118 interfaces with the computer BUS 2134 to provide quick RAM storage to the CPU 2102 during the execution of software programs such as the operating system application programs, and device drivers. More specifically, the CPU 2102 loads computer-executable process steps from the storage medium 2122 or other media into a field of the RAM 2118 to execute software programs. Data may be stored in the RAM 2118, where the data may be accessed by the computer CPU 2102 during execution.

The storage medium 2122 itself may include a number of physical drive units, such as a redundant array of independent disks (RAID), a floppy disk drive, a flash memory, a USB flash drive, an external hard disk drive, thumb drive, pen drive, key drive, a High-Density Digital Versatile Disc (HD-DVD) optical disc drive, an internal hard disk drive, a Blu-Ray optical disc drive, or a Holographic Digital Data Storage (HDDS) optical disc drive, an external mini-dual in-line memory module (DIMM) synchronous dynamic random access memory (SDRAM), or an external micro-DIMM SDRAM. Such computer readable storage media allow a computing device to access computer-executable process steps, application programs and the like, stored on removable and non-removable memory media, to off-load data from the device or to upload data onto the device. A computer program product, such as one utilizing a communication system may be tangibly embodied in storage medium 2122, which may include a machine-readable storage medium.

According to one example implementation, the term computing device, as used herein, may be a CPU, or conceptualized as a CPU (for example, the CPU 2102 of FIG. 21). In this example implementation, the computing device (CPU) may be coupled, connected, and/or in communication with one or more peripheral devices, such as display. In another example implementation, the term computing device, as used herein, may refer to a mobile computing device such as a smart phone, tablet computer, or smart watch. In this example implementation, the computing device may output content to its local display and/or speaker(s). In another example implementation, the computing device may output content to an external display device (e.g., over Wi-Fi) such as a TV or an external computing system.

In example implementations of the disclosed technology, a computing device may include any number of hardware and/or software applications that are executed to facilitate any of the operations. In example implementations, one or more I/O interfaces may facilitate communication between the computing device and one or more input/output devices. For example, a universal serial bus port, a serial port, a disk drive, a CD-ROM drive, and/or one or more user interface devices, such as a display, keyboard, keypad, mouse, control panel, touch screen display, microphone, etc., may facilitate user interaction with the computing device. The one or more I/O interfaces may be used to receive or collect data and/or user instructions from a wide variety of input devices. Received data may be processed by one or more computer processors as desired in various implementations of the disclosed technology and/or stored in one or more memory devices.

One or more network interfaces may facilitate connection of the computing device inputs and outputs to one or more suitable networks and/or connections; for example, the connections that facilitate communication with any number of sensors associated with the system. The one or more network interfaces may further facilitate connection to one or more suitable networks; for example, a local area network, a wide area network, the Internet, a cellular network, a radio frequency network, a Bluetooth enabled network, a Wi-Fi enabled network, a satellite-based network any wired network, any wireless network, etc., for communication with external devices and/or systems.

REFERENCES

-   [1] A. E. M. Vickers and R. L. Fisher, “Organ slices for the     evaluation of human drug toxicity,” Chem.-Biol. Interact., vol. 150,     no. 1, pp. 87-96, 2004. -   [2] H. Kamioka, T. Honjo, and T. Takano-Yamamoto, “A     three-dimensional distribution of osteocyte processes revealed by     the combination of confocal laser scanning microscopy and     differential interference contrast microscopy,” Bone, vol. 28, no.     2, pp. 145-149, 2001. -   [3] S. J. Mulligan and B. A. MacVicar, “Calcium transients in     astrocyte endfeet cause cerebrovascular constrictions,” Nature, vol.     431, pp. 195-199, September 2004. -   [4] A. Bussek, E. Wettwer, T. Christ, H. Lohmann, P. Camelliti,     and U. Ravens, “Tissue slices from adult mammalian hearts as a model     for pharmacological drug testing,” Cellular Physiol. Biochem., vol.     24, nos. 5-6, pp. 527-536, 2009. -   [5] I. Simon, C. R. Pound, A. W. Partin, J. Q. Clemens, and W. A.     Christens-Barry, “Automated image analysis system for detecting     boundaries of live prostate cancer cells,” Cytometry, vol. 31, no.     4, pp. 287-294, 1998. -   [6] K. Wu, D. Gauthier, and M. D. Levine, “Live cell image     segmentation,” IEEE Trans. Biomed. Eng., vol. 42, no. 1, pp. 1-12,     January 1995. -   [7] A. Dufour, V. Shinin, S. Tajbakhsh, N. Guillén-Aghion, J.-C.     Olivo-Marin, and C. Zimmer, “Segmenting and tracking fluorescent     cells in dynamic 3-D microscopy with coupled active surfaces,” IEEE     Trans. Image Process., vol. 14, no. 9, pp. 1396-1410, September     2005. -   [8] F. Yang, M. A. Mackey, F. Ianzini, G. Gallardo, and M. Sonka,     “Cell segmentation, tracking, and mitosis detection using temporal     context,” in Proc. Int. Conf. Med. Image Comput. Comput.-Assisted     Intervent., 2005, pp. 302-309. -   [9] D. Padfield, J. Rittscher, N. Thomas, and B. Roysam,     “Spatio-temporal cell cycle phase analysis using level sets and fast     marching methods,” Med. Image Anal., vol. 13, no. 1, pp. 143-155,     2009. -   [10] O. Dzyubachyk, W. Niessen, and E. Meijering, “A variational     model for level-set based cell tracking in time-lapse fluorescence     microscopy images,” in Proc. 4th IEEE Int. Symp. Biomed. Imag., Nano     Macro (ISBI), April 2007, pp. 97-100. -   [11] C. Zimmer, E. Labruyere, V. Meas-Yedid, N. Guillen, and J. C.     Olivo-Marin, “Segmentation and tracking of migrating cells in     videomicroscopy with parametric active contours: A tool for     cell-based drug testing,” IEEE Trans. Med. Imag., vol. 21, no. 10,     pp. 1212-1221, October 2002. -   [12] M. Maška, O. Danÿ ek, S. Garasa, A. Rouzaut, A. Muñoz-Barrutia,     and C. Ortiz-de Solorzano, “Segmentation and shape tracking of whole     fluorescent cells based on the Chan—Vese model,” IEEE Trans. Med.     Imag., vol. 32, no. 6, pp. 995-1006, June 2013. -   [13] M. Maška et al., “A benchmark for comparison of cell tracking     algorithms,” Bioinformatics, vol. 30, no. 11, pp. 1609-1617, 2014. -   [14] V. Ulman, M. Maška, and C. Ortiz-de-Solorzano, “An objective     comparison of cell-tracking algorithms,” Nature Methods, vol. 14,     pp. 1141-1152, October 2017. -   [15] D. Padfield, J. Rittscher, and B. Roysam, “Coupled minimum-cost     flow cell tracking for high-throughput quantitative analysis,” Med.     Image Anal., vol. 15, no. 4, pp. 650-668, 2011. -   [16] O. P. Hamill, A. Marty, E. Neher, B. Sakmann, and F. J.     Sigworth, “Improved patch-clamp techniques for high-resolution     current recording from cells and cell-free membrane patches,”     Pflügers Arch., vol. 391, no. 2, pp. 85-100, 1981. -   [17] G. J. Stuart, H. U. Dodt, and B. Sakmann, “Patch-clamp     recordings from the soma and dendrites of neurons in brain slices     using infrared video microscopy,” Pflügers Arch., vol. 423, nos.     5-6, pp. 511-518, 1993. -   [18] S. B. Kodandaramaiah, G. T. Franzesi, B. Y. Chow, E. S. Boyden,     and C. R. Forest, “Automated whole-cell patch-clamp     electrophysiology of neurons in vivo,” Nature Methods, vol. 9, pp.     585-587, May 2012. -   [19] I. Kolb, W. A. Stoy, E. B. Rousseau, O. A. Moody, A. Jenkins,     and C. R. Forest, “Cleaning patch-clamp pipettes for immediate     reuse,” Sci. Rep., vol. 6, October 2016, Art. no. 35001. -   [20] K. Li and T. Kanade, “Nonnegative mixed-norm preconditioning     for microscopy image segmentation,” in Information Processing in     Medical Imaging. Berlin, Germany: Springer, 2009, pp. 362-373. -   [21] U.S. Grain Standards Act Federal Standard. (Aug. 7, 1996).     Telecommunications: Glossary of Telecommunication Terms. [Online].     Available: www.its.bldrdoc.gov/fs-1037/fs-1037c.htm -   [22] E. B. Van Munster, L. J. Van Vliet, and J. A. Aten,     “Reconstruction of optical pathlength distributions from images     obtained by a wide-field differential interference contrast     microscope,” J. Microscopy, vol. 188, no. 2, pp. 149-157, 1997. -   [23] N. N. Kachouie, P. Fieguth, and E. Jervis, “Watershed     deconvolution for cell segmentation,” in Proc. 30th Annu. Int. Conf.     IEEE Eng. Med. Biol. Soc., August 2008, pp. 375-378. -   [24] O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolutional     networks for biomedical image segmentation,” in Proc. Int. Conf.     Med. Image Comput. Comput.-Assisted Intervent., 2015, pp. 234-241. -   [25] Z. Yin, R. Bise, M. Chen, and T. Kanade, “Cell segmentation in     microscopy imagery using a bag of local Bayesian classifiers,” in     Proc. IEEE Int. Symp. Biomed. Imag., Nano Macro, April 2010, pp.     125-128. -   [26] A. Kuijper and B. Heise, “An automatic cell segmentation method     for differential interference contrast microscopy,” in Proc. 19th     Int. Conf. Pattern Recognit. (ICPR), December 2008, pp. 1-4. -   [27] B. Obara, M. A. Roberts, J. P. Armitage, and V. Grau,     “Bacterial cell identification in differential interference contrast     microscopy images,” BMC Bioinf., vol. 14, no. 1, p. 134, 2013. -   [28] B. Heise, A. Sonnleitner, and E. P. Klement, “DIC image     reconstruction on large cell scans,” Microscopy Res. Techn., vol.     66, no. 6, pp. 312-320, 2005. -   [29] M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete,     and K. G. Larkin, “Using the Hilbert transform for 3D visualization     of differential interference contrast microscope images,” J.     Microscopy, vol. 199, no. 1, pp. 79-84, 2000. -   [30] Z. Yin and T. Kanade, “Restoring artifact-free microscopy image     sequences,” in Proc. IEEE Int. Symp. Biomed. Imag., Nano Macro,     March/April 2011, pp. 909-913. -   [31] E. J. Candès, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity     by reweighted 1 minimization,” J. Fourier Anal. Appl., vol. 14, nos.     5-6, pp. 877-905, 2008. -   [32] P. Garrigues and B. A. Olshausen, “Group sparse coding with a     Laplacian scale mixture prior,” in Proc. Adv. Neural Inf. Process.     Syst., 2010, pp. 676-684. -   [33] A. S. Charles, A. Balavoine, and C. J. Rozell, “Dynamic     filtering of time-varying sparse signals via 1 minimization,” IEEE     Trans. Signal Process., vol. 64, no. 21, pp. 5644-5656, November     2016. -   [34] L. A. Shepp and B. F. Logan, “The Fourier reconstruction of a     head section,” IEEE Trans. Nucl. Sci., vol. 21, no. 3, pp. 21-43,     June 1974. -   [35] A. Lehmussola, P. Ruusuvuori, J. Selinummi, T. Rajala, and O.     Yli-Harja, “Synthetic images of high-throughput microscopy for     validation of image analysis methods,” Proc. IEEE, vol. 96, no. 8,     pp. 1348-1360, August 2008. -   [36] D. Svoboda and V. Ulman, “Generation of synthetic image     datasets for time-lapse fluorescence microscopy,” in Image Analysis     and Recognition.Berlin, Germany: Springer, 2012, pp. 473-482. -   [37] S. Rajaram, B. Pavie, N. E. Hac, S. J. Altschuler, and L. F.     Wu, “SimuCell: A flexible framework for creating synthetic     microscopy images,” Nature Methods, vol. 9, pp. 634-635, June 2012. -   [38] R. F. Murphy, “Cellorganizer: Image-derived models of     subcellular organization and protein distribution,” Methods Cell     Biol., vol. 110, pp. 179-193, July 2012. -   [39] L. Martins, J. Fonseca, and A. Ribeiro, “'miSimBa'—A Simulator     of synthetic time-lapsed microscopy images of bacterial cells,” in     Proc. IEEE 4th Portuguese Meeting Bioeng. (ENBENG), February 2015,     pp. 1-6. -   [40] X. Lan, A. J. Ma, and P. C. Yuen, “Multi-cue visual tracking     using robust feature-level fusion based on joint sparse     representation,” in Proc. IEEE Conf. Comput. Vis. Pattern Recognit.,     June 2014, pp. 1194-1201. -   [41] X. Lan, A. J. Ma, P. C. Yuen, and R. Chellappa, “Joint sparse     representation and robust feature-level fusion for multi-cue visual     tracking,” IEEE Trans. Image Process., vol. 24, no. 12, pp.     5826-5841, December 2015. -   [42] X. Lan, S. Zhang, and P. C. Yuen, “Robust joint discriminative     feature learning for visual tracking,” in Proc. IJCAI, 2016, pp.     3403-3410. -   [43] X. Lan, P. C. Yuen, and R. Chellappa, “Robust mil-based feature     template learning for object tracking,” in Proc. AAAI, 2017, pp.     4118-4125. -   [44] J. Lee and C. J. Rozell, “Precision cell boundary tracking on     DIC microscopy video for patch clamping,” in Proc. Int. Conf.     Acoust., Speech, Signal Process. (ICASSP), New Orleans, La., USA,     March 2017, pp. 1048-1052. -   [45] N. Otsu, “A threshold selection method from gray-level     histograms,” Automatica, vol. 11, nos. 285-296, pp. 23-27, 1975. -   [46] L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total     variation based noise removal algorithms,” Phys. D, Nonlinear     Phenomena, vol. 60, nos. 1-4, pp. 259-268, 1992. -   [47] A. S. Charles and C. J. Rozell, “Spectral superresolution of     hyperspectral imagery using reweighted 1 spatial filtering,” IEEE     Geosci. Remote Sens. Lett., vol. 11, no. 3, pp. 602-606, March 2014. -   [48] J. Shen and T. F. Chan, “Mathematical models for local     nontextured inpaintings,” SIAM J. Appl. Math., vol. 62, no. 3, pp.     1019-1043, 2002. -   [49] Q. Wu et al., “Integration of autopatching with automated     pipette and cell detection in vitro,” J. Neurophysiol., vol. 116,     no. 4, pp. 1564-1578, 2016. -   [50] J. C. Russ and F. B. Neal, The Image Processing Handbook, 7th     ed. Boca Raton, Fla., USA: CRC Press, 2015. -   [51] E. Olson, “Particle shape factors and their use in image     analysis—Part 1: Theory,” J. GXP Compliance, vol. 15, no. 3, pp.     85-96, 2011. -   [52] M. Grant and S. Boyd. (March 2014). CVX: MATLAB Software for     Disciplined Convex Programming, Version 2.1. [Online]. Available:     cvxr.com/cvx -   [53] M. C. Grant and S. P. Boyd, “Graph implementations for     nonsmooth convex programs,” in Recent Advances in Learning and     Control (Lecture Notes in Control and Information Sciences), V.     Blondel, S. Boyd, and H. Kimura, Eds. New York, N.Y., USA:     Springer-Verlag, 2008, pp. 95-110. [Online]. Available:     stanford.edu/boyd/graph_dcp.html -   [54] S. R. Becker, E. J. Candes, and M. C. Grant, “Templates for     convex cone problems with applications to sparse signal recovery,”     Math. Program. Comput., vol. 3, no. 3, pp. 165-218, September 2011. -   [55] S. H. Chan, R. Khoshabeh, K. B. Gibson, P. E. Gill, and T. Q.     Nguyen, “An augmented Lagrangian method for total variation video     restoration,” IEEE Trans. Image Process., vol. 20, no. 11, pp.     3097-3111, November 2011. -   [56] M. Tao, J. Yang, and B. He, “Alternating direction algorithms     for total variation deconvolution in image reconstruction,” Dept.     Math., Nanjing Univ., Nanjing, China, Tech. Rep. TR0918, 2009. -   [57] L. Wen, D. Du, Z. Lei, S. Z. Li, and M.-H. Yang, “JOTS: Joint     online tracking and segmentation,” in Proc. IEEE Conf. Comput. Vis.     Pattern Recognit., June 2015, pp. 2226-2234. -   [58] Y. Yang and G. Sundaramoorthi, “Modeling self-occlusions in     dynamic shape and appearance tracking,” in Proc. IEEE Int. Conf.     Comput. Vis. (ICCV), December 2013, pp. 201-208. -   [59] Z. Yin and R. T. Collins, “Shape constrained figure-ground     segmentation and tracking,” in Proc. IEEE Conf. Comput. Vis. Pattern     Recognit., June 2009, pp. 731-738. -   [60] Z. Pincus and J. A. Theriot, “Comparison of quantitative     methods for cell-shape analysis,” J. Microscopy, vol. 227, no. 2,     pp. 140-156, 2007. -   [61] A. Lehmussola, P. Ruusuvuori, J. Selinummi, H. Huttunen, and O.     Yli-Harja, “Computational framework for simulating fluorescence     microscope images with cell populations,” IEEE Trans. Med. Imag.,     vol. 26, no. 7, pp. 1010-1016, July 2007. -   [62] D. Svoboda, M. Kozubek, and S. Stejskal, “Generation of digital     phantoms of cell nuclei and simulation of image formation in 3D     image cytometry,” Cytometry Part A, vol. 75A, no. 6, pp. 494-509,     2009. -   [63] K. Perlin, “An image synthesizer,” Siggraph Comput. Graph.,     vol. 19, no. 3, pp. 287-296, 1985. -   [64] A. Lehmussola, J. Selinummi, P. Ruusuvuori, A. Niemisto, and O.     Yli-Harja, “Simulating fluorescent microscope images of cell     populations,” in Proc. IEEE 27th Annu. Int. Conf. Eng. Med. Biol.     Soc. (EMBS), January 2006, pp. 3153-3156. -   [65] Mathworks. (2016). Creating a Gallery of Transformed Images.     [Online]. Available:     www.mathworks.com/help/images/examples/creating-a-gallery-of-transformed-images.html#zmw57dd0e4163

While several possible embodiments are disclosed above, embodiments of the present disclosure are not so limited. These exemplary embodiments are not intended to be exhaustive or to unnecessarily limit the scope of the disclosure, but instead were chosen and described in order to explain the principles of the present disclosure so that others skilled in the art may practice the disclosure. Indeed, various modifications of the disclosure in addition to those described herein will become apparent to those skilled in the art from the foregoing description. Such modifications are intended to fall within the scope of the appended claims.

All patents, applications, publications, test methods, literature, and other materials cited herein are hereby incorporated by reference in their entirety as if physically present in this specification. 

What is claimed is:
 1. A system comprising: at least one processor; and at least one memory having stored thereon instructions that, when executed by the at least one processor, control the at least one processor to: receive image data of a sequence of images, and a current image of the sequence of images being after a previous image in the sequence of images, each of the current and previous images including a cell; filter the current image to remove noise; iteratively deconvolve the filtered current image to identify edges of the cell within the current image based on determined edges of the cell within the previous image; and segment the deconvolved current image to determine edges of the cell within the current image.
 2. The system of claim 1, wherein the instructions, when executed by the at least one processor, further control the at least one processor to: identify, within the current image, a subset of the current image containing the cell, deconvolving being performed only on the identified subset of the current image.
 3. The system of claim 1, wherein the instructions, when executed by the at least one processor, control the at least one processor to iteratively deconvolve the filtered current image by: determining an estimated edge that minimizes a cost function; adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.
 4. The system of claim 3, wherein the cost function comprises a first term corresponding to a predictive error between the current image and an image predicted from the estimated edge, and a second term corresponding to a connectivity determination of the estimated edge within the current image.
 5. The system of claim 4, wherein the adjusted weights of the cost function modify the connectivity determination of the estimated edge within the current image.
 6. The system of claim 5, wherein the determined edges of the cell within the previous image impact the adjusted weights.
 7. The system of claim 1, wherein the instructions, when executed by the at least one processor, control the at least one processor to iteratively deconvolve the filtered current image by: iteratively estimate an edge that minimizes a cost function utilizing alternating direction method of multipliers (ADMM); adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.
 8. The system of claim 1, wherein the instructions, when executed by the at least one processor, further control the at least one processor to output instructions to an articulating arm to position an instrument proximal to the determined edge of the current image.
 9. The system of claim 8, wherein the instrument comprises one or more of: an electrode; an injector; and a manipulation instrument.
 10. The system of claim 1, wherein the instructions, when executed by the at least one processor, further control the at least one processor to: set the current image as the previous image; set a next image in the sequence of images as the current image; and repeat the filtering, iteratively deconvolving, and segmenting.
 11. The system of claim 10, wherein the sequence of image comprises a live video, and the edges of the cell within the current image are determined in near real-time.
 12. A method comprising: receiving image data of a sequence of images, and a current image of the sequence of images being after a previous image in the sequence of images, each of the current and previous images including a cell; filtering the current image to remove noise; iteratively deconvolving the filtered current image to identify edges of the cell within the current image based on determined edges of the cell within the previous image; and segmenting the deconvolved current image to determine edges of the cell within the current image.
 13. The method of claim 12 further comprising identifying, within the current image, a subset of the current image containing the cell, deconvolving being performed only on the identified subset of the current image.
 14. The method of claim 12 further comprising iteratively deconvolving the current image by: determining an estimated edge that minimizes a cost function; adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.
 15. The method of claim 14, wherein the cost function comprises a first term corresponding to a predictive error between the current image and an image predicted from the estimated edge, and a second term corresponding to a connectivity determination of the estimated edge within the current image.
 16. The method of claim 15, wherein the adjusted weights of the cost function modify the connectivity determination of the estimated edge within the current image, and the determined edges of the cell within the previous image impact the adjusted weights.
 17. The method of claim 12 further comprising deconvolving the filtered current image by: iteratively estimate an edge that minimizes a cost function utilizing alternating direction method of multipliers (ADMM); adjusting weights of the cost function based on the estimated edge; and repeating the determining and adjusting.
 18. The method of claim 12 further comprising moving an articulating arm to position an instrument proximal to the determined edge of the current image.
 19. The method of claim 12 further comprising: setting the current image as the previous image; setting a next image in the sequence of images as the current image; and repeating the filtering, iteratively deconvolving, and segmenting.
 20. The method of claim 19, wherein the sequence of image comprises a live video, and the edges of the cell within the current image are determined in near real-time. 